A note on lower bounds of decay rates for solutions to the Navier-Stokes equations in the norms of Besov spaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F14%3A00227614" target="_blank" >RIV/68407700:21110/14:00227614 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.na.2013.11.007" target="_blank" >http://dx.doi.org/10.1016/j.na.2013.11.007</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.na.2013.11.007" target="_blank" >10.1016/j.na.2013.11.007</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A note on lower bounds of decay rates for solutions to the Navier-Stokes equations in the norms of Besov spaces

Popis výsledku v původním jazyce

We study the lower bounds of decay rates for turbulent solutions to the Navier-Stokes equations in the norms of Besov spaces. We focus on solutions satisfying $0 < liminf_{t rightarrow infty} t^gamma ||u(t)|| le limsup_{t rightarrow infty} t^gamma ||u(t)|| < infty$ for some $gamma in (0,5/4]$ and prove among others that such solutions, measured in the norm of the Besov space $dot{B}^{-2gamma}_{2,infty}$, are estimated for large times from below by some positive constant. These estimates stem from sufficiently fast rate of large time energy concentration in low frequencies occurring in the studied solutions. Our results have simple proofs and improve and extend substantially the results published by Miyakawa in cite{Mi} and by Schonbek and Wiegner in cite{SchWi}

Název v anglickém jazyce

A note on lower bounds of decay rates for solutions to the Navier-Stokes equations in the norms of Besov spaces

Popis výsledku anglicky

We study the lower bounds of decay rates for turbulent solutions to the Navier-Stokes equations in the norms of Besov spaces. We focus on solutions satisfying $0 < liminf_{t rightarrow infty} t^gamma ||u(t)|| le limsup_{t rightarrow infty} t^gamma ||u(t)|| < infty$ for some $gamma in (0,5/4]$ and prove among others that such solutions, measured in the norm of the Besov space $dot{B}^{-2gamma}_{2,infty}$, are estimated for large times from below by some positive constant. These estimates stem from sufficiently fast rate of large time energy concentration in low frequencies occurring in the studied solutions. Our results have simple proofs and improve and extend substantially the results published by Miyakawa in cite{Mi} and by Schonbek and Wiegner in cite{SchWi}

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2014

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Nonlinear Analysis: Theory, Methods & Applications

ISSN

0362-546X

e-ISSN

—

Svazek periodika

97

Číslo periodika v rámci svazku

březen

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

6

Strana od-do

228-233

Kód UT WoS článku

000329114400019

EID výsledku v databázi Scopus

—